循环载荷下接触安定问题的数值方法及工程应用
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摘要
接触体表面强化(喷丸、涂层)层的疲劳裂纹萌生寿命的研究，是当前齿轮、轴承等接触件失效分析中的前沿课题。它具有重要而广泛的工程背景。在国家“航空基金”、“总装预研基金”等课题的资助下，本文以接触体安定分析与接触表面层疲劳裂纹萌生寿命预测一般算法研究为手段，深入、系统研究了接触体安定分析的数值理论和计算方法，全面研究了影响航空齿轮表面强化层失效的原因并提出了齿轮表面强化层裂纹萌生寿命的预测方法。
本文针对接触表面层的强化与疲劳失效问题，提出通过研究接触表面层在循环载荷作用下的安定特性，来建立强化设计与疲劳评估准则。研究中，围绕强化后接触表面疲劳问题，从强化模型选择、接触表层安定性存在的条件及其失效规律，进行了详细的概念定义、定理证明及推论演算等理论工作，为接触表面层安定性的数值模拟和疲劳分析奠定了理论基础。
提出了接触体安定性下限分析的线性规划法和直接叠代法。这些方法各有创新，其特点是计算速度快、收敛性好及精度可靠，计算规模避免了弹塑性随动强化分析的非线性的影响，并使弹塑性问题转化为残余问题和线弹性问题，适用于滚动、滚滑及滑动接触失效分析，从而有效地解决了接触体安定性分析与裂纹萌生寿命预测的实际问题，也是本文对表面强化接触失效的安定分析成为可能。
对二维滚滑弹塑性接触的安定状态，建立循环载荷下接触安定状态分析的计算机应用程序，并进行了残余应变和残余应力的分析计算。研究表明安定状态随载荷的大小而变化，其残余应力和应变累积的大小与外加载荷成正比，并对计算中的一些问题进行了分析探讨。
利用Chaboche的材料模型，研究了航空齿轮韧性材料在弹、塑性安定下的轮齿接触疲劳裂纹萌生准则，该研究结果与相关的齿轮实验结果比较分析表明：塑性安定下的疲劳裂纹萌生预测方法预测航空齿轮的萌生寿命是较安全的。
本文所提出的理论分析方法具有科学、经济和实用等优点，对于各种接触元件的设计、预测及失效评估具有指导作用。
At present an important subject is researched on prediction methods of the initiation life of rolling/sliding contact fatigue of surface hardening layer based on shakedown theories under cycle contact loading for the strategies of applications of contact element, such as gears, bearings, and railroad rails. In this thesis, the strain-hardening model of contact surface layer, the numerical theories and computational methods for shakedown analyses of contact body are systematically studied and applied to the aero-gear. The mentality is that the effects of the surface hardening and contact fatigue on contact surface layer under cycle contact loading are investigated by using shakedown analysis methods considering in a quantitative way the details of stress-inelastic strain responses, residual stress and residual strain computations. The experiment on the conclusion of shakedown analysis with the direct analysis method was conducted for proving residual stress of contact surface layer of the rolled specimen.The
paper concerns itself on the following specific aspects:
1. Studying on the shakedown theories and plastic deformation of contact surface layer
The shakedown of contact surface layer is related to the strain-hardening models of materials, such as isotropic hardening, kinematic-hardening, and mixed-hardening. The existing results based on experiments and theory show that the shearing strain behavior of contact surface layer caused by friction can be comparatively described with kinematic-hardening. The shakedown conditions of contact surface layer based on kinematic-hardening model was given. In this thesis, the research result was shown, kinematic-hardening contact surface layer could not involve incremental collapse, but could only cause alternating plasticity. And it also have been shown that the back stresses have effect on the shakedown limit of contact surface layer, however, there are some difficulties on the definition of back stress as the "center" of the yield surface in the Cauchy space. So, the back stress tensor is taked usually in the Lagrangian stress space.
2. Studying on the shakedown analysis methods of contact surface layer
A series of efficient computational approaches, for example, a direct analysis method and a line programming, for the shakedown analysis and limit is proposed, which is used to investigate the effect of strain hardening and residual stress on the shakedown limit of contact element. The direct analysis method has more efficient
than the line programming for the shakedown analysis of contact surface layer, therefore, the mentality of shakedown analysis of contact surface layer was introduced based on the direct analysis method as follows:
First, the direct method for shakedown analysis was presented and its application to a two-dimensional rolling/sliding contact problem was demonstrated. The direct method consists of operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains, and an incremental projection method to determine the eigenstrain. Second, the direct analysis method was applied to determine the residual stress of rolling/sliding contact between cylinder and plane. More over the limit of shakedown load of contact surface layer was computed with different friction affection. Finals, rolling and sliding contact between cylinder and plane was analyzed with ANSYS? Four contact state depending on rate of rolling/sliding between the couple of contact element were studied based on Hertz contact model, and the results was shown that the rate of slide would affect the distribution of pressure in contact area and stress in the half plane.
3. Studying on prediction methods of the initiation life of aero-gear using shakedown analysis methods
In order to directly consider in a quantitative way the details of stress-inelastic strain responses, residual stress and residual strain computations, fatigue crack initiation life was evaluated in aero-gear by using th
本文针对接触表面层的强化与疲劳失效问题，提出通过研究接触表面层在循环载荷作用下的安定特性，来建立强化设计与疲劳评估准则。研究中，围绕强化后接触表面疲劳问题，从强化模型选择、接触表层安定性存在的条件及其失效规律，进行了详细的概念定义、定理证明及推论演算等理论工作，为接触表面层安定性的数值模拟和疲劳分析奠定了理论基础。
提出了接触体安定性下限分析的线性规划法和直接叠代法。这些方法各有创新，其特点是计算速度快、收敛性好及精度可靠，计算规模避免了弹塑性随动强化分析的非线性的影响，并使弹塑性问题转化为残余问题和线弹性问题，适用于滚动、滚滑及滑动接触失效分析，从而有效地解决了接触体安定性分析与裂纹萌生寿命预测的实际问题，也是本文对表面强化接触失效的安定分析成为可能。
对二维滚滑弹塑性接触的安定状态，建立循环载荷下接触安定状态分析的计算机应用程序，并进行了残余应变和残余应力的分析计算。研究表明安定状态随载荷的大小而变化，其残余应力和应变累积的大小与外加载荷成正比，并对计算中的一些问题进行了分析探讨。
利用Chaboche的材料模型，研究了航空齿轮韧性材料在弹、塑性安定下的轮齿接触疲劳裂纹萌生准则，该研究结果与相关的齿轮实验结果比较分析表明：塑性安定下的疲劳裂纹萌生预测方法预测航空齿轮的萌生寿命是较安全的。
本文所提出的理论分析方法具有科学、经济和实用等优点，对于各种接触元件的设计、预测及失效评估具有指导作用。
At present an important subject is researched on prediction methods of the initiation life of rolling/sliding contact fatigue of surface hardening layer based on shakedown theories under cycle contact loading for the strategies of applications of contact element, such as gears, bearings, and railroad rails. In this thesis, the strain-hardening model of contact surface layer, the numerical theories and computational methods for shakedown analyses of contact body are systematically studied and applied to the aero-gear. The mentality is that the effects of the surface hardening and contact fatigue on contact surface layer under cycle contact loading are investigated by using shakedown analysis methods considering in a quantitative way the details of stress-inelastic strain responses, residual stress and residual strain computations. The experiment on the conclusion of shakedown analysis with the direct analysis method was conducted for proving residual stress of contact surface layer of the rolled specimen.The
paper concerns itself on the following specific aspects:
1. Studying on the shakedown theories and plastic deformation of contact surface layer
The shakedown of contact surface layer is related to the strain-hardening models of materials, such as isotropic hardening, kinematic-hardening, and mixed-hardening. The existing results based on experiments and theory show that the shearing strain behavior of contact surface layer caused by friction can be comparatively described with kinematic-hardening. The shakedown conditions of contact surface layer based on kinematic-hardening model was given. In this thesis, the research result was shown, kinematic-hardening contact surface layer could not involve incremental collapse, but could only cause alternating plasticity. And it also have been shown that the back stresses have effect on the shakedown limit of contact surface layer, however, there are some difficulties on the definition of back stress as the "center" of the yield surface in the Cauchy space. So, the back stress tensor is taked usually in the Lagrangian stress space.
2. Studying on the shakedown analysis methods of contact surface layer
A series of efficient computational approaches, for example, a direct analysis method and a line programming, for the shakedown analysis and limit is proposed, which is used to investigate the effect of strain hardening and residual stress on the shakedown limit of contact element. The direct analysis method has more efficient
than the line programming for the shakedown analysis of contact surface layer, therefore, the mentality of shakedown analysis of contact surface layer was introduced based on the direct analysis method as follows:
First, the direct method for shakedown analysis was presented and its application to a two-dimensional rolling/sliding contact problem was demonstrated. The direct method consists of operator split technique, which transforms the elastic-plastic problem into a purely elastic problem and a residual problem with prescribed eigenstrains, and an incremental projection method to determine the eigenstrain. Second, the direct analysis method was applied to determine the residual stress of rolling/sliding contact between cylinder and plane. More over the limit of shakedown load of contact surface layer was computed with different friction affection. Finals, rolling and sliding contact between cylinder and plane was analyzed with ANSYS? Four contact state depending on rate of rolling/sliding between the couple of contact element were studied based on Hertz contact model, and the results was shown that the rate of slide would affect the distribution of pressure in contact area and stress in the half plane.
3. Studying on prediction methods of the initiation life of aero-gear using shakedown analysis methods
In order to directly consider in a quantitative way the details of stress-inelastic strain responses, residual stress and residual strain computations, fatigue crack initiation life was evaluated in aero-gear by using th
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